Answer: Graph (C) is the correct graph, Its image is attached below.
Step-by-step explanation: We are given to select the correct graph for the following quadratic function :
[tex]f(x)=(x+3)(x-2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The zeroes of the function (i) are given by
[tex]f(x)=0\\\\\Rightarrow (x+3)(x-2)=0\\\\\Rightarrow x+3=0,~~~~~x-2=0\\\\\Rightarrow x=-3,~2.[/tex]
That is, the graph of the function f(x) crosses the X-axis at x = -3 and x = 2.
From the given four graphs, we see that the third graph meets the X-axis at the points x = -3 and x = 2.
Therefore, the correct graph is the graph (C). Its image is attached below.
